COURSE ON MODEL THEORY
- P. Clark
- Mathematics
- 2012
Introduction 2 0.1. Some theorems in mathematics with snappy model-theoretic proofs 2 1. Languages, structures, sentences and theories 2 1.1. Languages 2 1.2. Statements and Formulas 5 1.3.…
Factorization in Integral Domains I
- P. Clark
- Mathematics
- 2009
Definition 1.1. For r, s ∈ R, we say that r divides s (written r|s) if there exists a t ∈ R such that s = tr. An element u ∈ R is a unit if it has a multiplicative inverse, i.e. if there exists an…
COMPUTATION ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION
- P. Clark, Patrick Corn, Alex Rice, James Stankewicz
- Mathematics, Computer Science
- 23 July 2013
We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number elds of degree 1-13. Addi- tionally we describe the algorithm used to compute these…
Torsion points and Galois representations on CM elliptic curves
- Abbey Bourdon, P. Clark
- MathematicsPacific Journal of Mathematics
- 10 December 2016
We prove several results on torsion points and Galois representations for complex multiplication (CM) elliptic curves over a number field containing the CM field. The first, a close relative of a…
On Zeros of a Polynomial in a Finite Grid
- A. Bishnoi, P. Clark, Aditya Potukuchi, John R. Schmitt
- Mathematics, Computer ScienceCombinatorics, probability & computing
- 25 August 2015
The Alon–Füredi theorem is applied to quickly recover – and sometimes strengthen – old and new results in finite geometry, including the Jamison–Brouwer–Schrijver bound on affine blocking sets.
The Instructor’s Guide to Real Induction
- P. Clark
- Mathematics, PhilosophyMathematics Magazine
- 5 August 2012
Real induction is introduced, a proof technique analogous to Mathematical Induction but applicable to statements indexed by an interval on the real line, and inductive principles in arbitrary ordered sets are pursued.
Algebraic curves uniformized by congruence subgroups of triangle groups
We construct certain subgroups of hyperbolic triangle groups which we call \congruence" subgroups. These groups include the classical congruence subgroups of SL2(Z), Hecke triangle groups, and 19…
The period–index problem in WC-groups I: elliptic curves
- P. Clark
- Mathematics
- 7 June 2004
DIRICHLET SERIES
- P. Clark
- Mathematics
- 2008
This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty…
The Combinatorial Nullstellensätze Revisited
- P. Clark
- Mathematics, PhysicsElectronic Journal of Combinatorics
- 13 May 2014
The celebrated Combinatorial Nullstellensatze of N. Alon is revisited and further explored in several different directions.
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